Inputting characters appends them to the regex and continues incremental search. "BackSpace" removes a character from the regex, "Up" and "Down" search upwards/downwards in the scrollback buffer, "End" jumps to the bottom. "Escape" leaves search mode and returns to the point where search was started, while "Enter" or "Return" stay at the current position and additionally stores the first match in the current line into the primary selection if the "Shift" modifier is active.
The regex defaults to ``(?i)'', resulting in a case-insensitive search. To get a case-sensitive search you can delete this prefix using "BackSpace" or simply use an uppercase character which removes the ``(?i)'' prefix.
See perlre for more info about perl regular expression syntax.